Enlargement and area

Learning Objective:

• we are learning to predict the effects of enlargement on the area of 2D shapes

Investing:

• This is useful because when you use scale drawings and maps you are using a scale factor and enlargement and you may need to find areas from these diagrams.
• A functional (real-life) application is finding the area of carpet if you know the area of a plan of a room at a given scale factor
• This skill leads to converting units of area
• This could help you if you want to work in architecture, interior design, farming, industrial design

Preparing:

• Can you already enlarge a shape using a scale factor and centre of enlargement?
• Before you start you need to know how to find the area of simple 2D shapes
• You will have a deeper understanding if you also know a bit about ratios

Discovering:

• Can you figure it out yourself from these examples?

• Compare the areas of the small rectangle with the larger rectangle
• Consider making a table of values
• What is the area factor for a length factor 2?
• For length factor 3?
• And 4?

• What's the pattern to this?

• What will the area scale factor be for a length factor of 9?
• What about 10?

Discussing:

• What would this one be? Tell your learning partner. Convince them you're right.
• Explain how you know.
• How would you explain this to someone who was new to it?

Explaining:

• Why does this work?

Developing and extending:

• What will happen to the volume of 3D shapes that are enlarged?